>>13929391Basic model theory explores the relationship between theories (meaning: sets of logical axioms) and their models (meaning: sets equipped with operations that obey the rules in the axioms). For example the theory could be the theory could be the usual set of group axioms; then its models are the objects which obey these axioms, i.e. groups. You explore the basic questions about how to move back and forth between theories and models, does a theory always have a model, can it have two different models, etc. More advanced model theory often deals with the higher infinite (e.g. Morley's categoricity theorem). Then more modern model theory is often geared to studying specific problems in other fields such as number theory.
>chang and keislerThat's a pretty old book, which may be a good thing or a bad thing depending on your point of view. It's thoroughly classical in its treatment and for that reason I find it easy to read.
